[EM] Voting Criteria 101, Four Criteria

Sun Jun 16 14:36:14 PDT 2013

Re: Majority Criteria:

To be honest, I am worried that some (or all) of your history lesson
regarding Arrow might not have landed as well as it should in my brain. I
can say that one of the things I may need help on is the wording of the
criteria, so if "preferred" is not the right word, then we should use
something else.

However, I *think* the base idea is the idea that if over 50% of a group
want a candidate to win, they should get that candidate.  What is more murky
to me - and perhaps more than me - is how you decide whether or not that is
being violated in systems that are more complex.

I guess I would say at a minimum, that if one is using Range Voting (which I
think you are saying is called Score Voting by the list; freely assign a
score of 0 to the maximum amount to each candidate (say 100), the candidate
with the greatest aggregate score wins) let me see how this might fail.
Let's say out of 1000 people 550 give candidate A scores of "100". Then
let's say that 700 people give candidate B scores of "80" each. Let's also
say that everyone else falls short of either of those totals.  A gets 55,000
total, B gets 56,000.  B wins.

On the one hand, one could say in one sense this violates Majority, but in
another sense one could perhaps with even more justification claim that B
actually has the larger majority.  Or maybe to put another way, Majority
criteria only applies to voters when the system is one person, 1 vote -
others perhaps Majority criteria applies to *votes*, not voters.

In other words, maybe Majority criteria should be worded thusly: If one
candidate is preferred by an absolute majority of *votes*, then that
candidate must win.

In which case it (I think) becomes even more obvious and pointless as a
criteria (as any system that gave the victory to people who get less votes,
however we are counting and measuring votes, would make no sense, I think.)

>>Name: Participation

>>Description: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B

>>Thoughts:  This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely

>>harms your interests. Also, any voting system that would fail
Participation would be I think fragile and react in not always 

>>predictable ways - like IRV. SO this seems to me to be a solid
requirement, that I can't imagine a system that failed this 

>>Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.

>You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the 

>direction of preference, not its strength; and so it is inevitably biased
towards preferential systems, and dooms you to live 

>within the limits set by Arrow's theorem. My two favorite systems - SODA
voting and the as-yet-unnamed version of 

>Bucklin - both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some 

>weakened version of the criterion.

I don't understand how a bias exists here. In every case I can currently
imagine, if an election as it stands has A winning, and one more ballot is
added which still prefers A to B, why should that ever cause the winner to
change to B?

Range/Score Voting: If A is winning, and the following ballot was added
(A:90, B:89) A would still be winning.  If IRV is being used and the
following ballot is added (D first place, A second place, B third place) we
wouldn't want B to suddenly be beating A. (Although in IRV I guess it could
happen, but the point is that we wouldn't want it to, right?)

This seems to be a serious issue. Whatever the voting method, if A is
currently winning, and one more ballot gets added that happens to favor A
with relation to B, how could it EVER be a good thing if B somehow becomes
the winner through the addition of that ballot?

I don't understand what bias has to do with the answer to that question?

Also, how could Bucklin (as I understand it) *ever* fail this one? Because a
ballot added that favors A to B under Bucklin would at minimum increase A by
the same amount as B, possibly more, but would *never* increase B more than
A, else the ballot could not be said to prefer A over B, right?

>> IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate 

>>can inevitably change the absolute ranking levels of existing candidates.
I think that IIA is certainly a nice thing to pass, \

>>but I'd hesitate to make it a sine qua non.

Independence of Irrelevant Alternative (IIA): Adding a new candidate B to an
election that previously A would have won must not cause anyone apart from A
or B to win.  That is, if A would have won before B was added to the ballot,
C must not win now.

Again, I seem to be missing something here.  If you are running an election
with whatever method, and A would win, but then B enters the race, I can get
A still winning.  I can get B leaping ahead somehow and winning.  What I
cannot understand is how a candidate that A was beating before B's entry,
somehow A now loses to. At least I cannot understand how any system that
fails this criteria could still be worth considering - how the outcome of A
beating C *until* B enters the race, after which C wins, is desirable. Is
there some example that explain how this turn of events could be somehow
fair or sensible?

Independence of Clones: since you are saying that IoC is not equivalent with
IIA, I will take up IoC independently along the way in a later set of
criteria.

I still am curious about this question:

Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandating the other - for example, a system with IIA must
also fulfill Participation, or vice versa?

Thanks for your time and help - and please, anyone who wants to chime in,
please do so, this is not just a conversation between myself and Jameson,
but between me and the community her.

Thanks! :)

-Benn Grant

eFix Computer Consulting

 <mailto:benn at 4efix.com> benn at 4efix.com

603.283.6601

From: Jameson Quinn [mailto:jameson.quinn at gmail.com] 
Sent: Sunday, June 16, 2013 4:44 PM
To: Benjamin Grant
Cc: election-methods at lists.electorama.com
Subject: Re: [EM] Voting Criteria 101, Four Criteria

2013/6/16 Benjamin Grant <benn at 4efix.com <mailto:benn at 4efix.com> >

...I would like to explain what I understand about some of these voting
criteria, a few at a time...

Thanks for doing this, and again, welcome. 

Name: Plurality

Description: If A gets more "first preference" ballots than B, A must not
lose to B.

Thoughts: If I understand this correctly, this is not a critical criteria to
my way of thinking.  Consider an election with 10 candidates. A gets 13% of
the first place votes, more than any other single candidate. And yet B gets
8% of the first place votes, and 46% of the second place votes. It seems
obvious to me that B "ought" to win. And yet, in this circumstance, this
violates the above Plurality Criterion. Therefor is seems to be that the
Plurality Criterion is not useful, to my way of thinking.

I think that most here would agree with what you've said.

Name: Majority

Description: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.

Presumably, by "preferred", you mean "preferred over all others". This
definition is actually a bit controversial. I'll explain, but I have to go
back a bit. Note that all that follows is my personal opinion; it's far too
opinionated to pass muster at Wikipedia, and though I suspect that some here
would agree with most of it, I'm also sure that others will chime in to
debate me on some points.

The modern science of voting theory begins with Kenneth Arrow in the 1950s.
I happen to be reading Kuhn (The Structure of Scientific Revolutions) at the
moment, so I'll use his terms. Before Arrow, the study of single-winner
voting systems was disorganized and unscientific; though figures such as
Maurice Duverger and Duncan Black had important insights into the incentives
of plurality on parties and voters, they could offer little guidance as to
how to improve the situation. Arrow offered the first paradigm for the
field. The Arrovian paradigm is essentially preferential, and it tends to
lead toward Condorcet systems as being "best". 

>From its very beginning, Arrow's own theorem marked sharp limits to how far
you could go within his paradigm. Nonetheless, as Kuhn quotes from Bacon,
"error leads to truth more quickly than confusion"; that is, even a flawed
paradigm is immensely more productive than prescientific disorganization.
For instance, the important Gibbard-Satterthwaite theorem on strategy
followed close on the heels of Arrow's result.

Since Arrow, there have been other paradigms advanced. Around 1980, Steven
Brams suggested Approval Voting, a simple idea which prior to that had been
used but never theorized. This was clearly a step out of the Arrovian
paradigm, but it didn't quite yet offer an alternative basis for further
research and refinement. Donald Saari then reacted against approval by
advancing a paradigm based on ordinal ballots and mathematical symmetry (and
thus, Borda voting); in my opinion, his willful ignorance of strategic
issues makes his way of thinking ultimately counterproductive, though some
of the tools he created are useful.

So the first person to offer a truly fertile alternative to the Arrovian
paradigm was, in my opinion, Warren Smith (active on this list), with his
1999 paper on Range Voting. This system, now mostly called Score Voting,
goes beyond approval to allow fractional ratings. The division between
Arrovian, preferential systems, and Score-like systems has been expressed
using multiple terms: ranked versus rated (with rated systems sometimes
further subdivided into rated or graded); ordinal versus cardinal;
preferential versus ???; and my own favorite terms, comparative versus
evaluative.

Since Smith, there has also been work in yet another paradigm, that of
delegation. The DemoEx party in Sweden, the study of Asset voting, liquid
democracy, delegable proxy, delegated yes-no (DYN), the revival of interest
in Dodgson's 19th-century proposal for delegated proportional
representation, and most recently my own proposal Simple
Optionally-delegated Approval (SODA) all lie in this line of inquiry.

Still, as always, there are some who continue to mine the vein of the old
Arrovian paradigm, and it can't be said that that vein is entirely played
out. The new paradigms also remain much less well-established academically;
for instance, Smith's seminal paper has never been published in a
peer-reviewed journal.

....

So all of that history is a backdrop for the debate over how to apply the
definitions of such criteria as Majority and Mutual Majority to evaluative
systems. Your definition of Majority uses the word "preferred", which
inevitably biases it towards ranked thinking. An advocate for evaluative
systems, like myself, would argue that it would be better to say "voted as
favorably as possible". This distinction makes no difference at all for a
comparative system - a candidate who is preferred over all others is, by
definition, at the very top of any purely comparative ballot - but it allows
a level playing field on which evaluative systems can aspire to pass this
criterion as well. Of course, partisans of the comparative Arrovian paradigm
argue back with what seem to me to be unproductive semantic arguments: the
criteria were originally defined in an earlier era, with reference to
comparative systems, so any extension of them to cover evaluative ones is
argued as illegitimate.

Thoughts: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him, any
other approach would seem to create minority rule? I guess a challenge to
this criteria might be the following: using Range Voting,

(Note: these days the term Score Voting is preferred.)

A gets a 90 range vote from 60 out of 100 voters, while B gets an 80 from 80
out of 100 voters. A's net is 5400, but B's net is 6400, so B would win
(everyone else got less).  Does this fail the Majority Criterion, because A
got a higher vote from over half, or does it fulfill Majority because B's
net was greater than A's net??

Your example uses the ranked definition of the majority criterion. In the
rated definition I'd favor, neither group of voters is rating their
candidate at the top rating, so the majority criterion simply does not
apply. But simply change the the rating of A proponents from 90 to 100, and
the rated definition applies, so you've shown that Score voting doesn't pass
majority under any definition. A score proponent would argue that a win by B
would be the best result in this situation, because it would (probably)
maximize total social utility; the large extra utility for the minority who
prefer B is more than the small loss of utility for the majority who prefer
A.

Name: Participation

Description: If a ballot is added which prefers A to B, the addition of the
ballot must not change the winner from A to B

Thoughts:  This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely harms your interests.
Also, any voting system that would fail Participation would be I think
fragile and react in not always predictable ways - like IRV. SO this seems
to me to be a solid requirement, that I can't imagine a system that failed
this Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.

You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the direction of preference,
not its strength; and so it is inevitably biased towards preferential
systems, and dooms you to live within the limits set by Arrow's theorem. My
two favorite systems - SODA voting and the as-yet-unnamed version of Bucklin
- both fail this criterion, though I would argue they do so in relatively
rare and minor ways, and both satisfy some weakened version of the
criterion.

Name: Independence of Irrelevant Alternatives (IIA)

Description: Adding a new candidate B to an election that previously A would
have won must not cause anyone apart from A or B to win.  That is, If A
would have won before B was added to the ballot, C must not win now.

Thoughts:  This also seems fairly non-controversial. This I think is the
repudiation of the spoiler effect - that just because Nader enters the race
shouldn't disadvantage the candidate that would have won before that
happened.  This would seem (to me) to also be a good Criterion to hold to in
order to encourage more than just two Candidates/Parties always dominating
the scene.  I wonder what the downside would be to strongly embracing this
criteria?

IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate can inevitably change the
absolute ranking levels of existing candidates. I think that IIA is
certainly a nice thing to pass, but I'd hesitate to make it a sine qua non.

Question: It seems to me that another criterion I have heard of -
Independence of Clones(IoC) - is a subset of IIA, that if a system satisfies
IIA, it would have to satisfy the Independence of Clones criterion as well -
is that correct? If not, what system what satisfy IoC but *not* satisfy IIA?

Not quite. A system which satisfied IoC could, in theory, shift from clone
X1 to X2 when another candidate (either an X3 or a Y3) entered the race,
which would violate IIA. And a system which satisfied IIA could, in
principle, shift from clone X1 to a newly-entering clone Y2, even though a
clone Y1 had already been in the race. I'm not offhand aware of which
systems would fall into these corners of the Venn diagram, but you are
mostly right: the large majority of systems which pass IoC also pass IIA.

Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandate the other - for example, a system with IIA must also
fulfill Participation, or vice versa?

So let me stop there for now - I know there are other Criteria, but let me
pause so you guys can tell me what I am getting right and what I am getting
wrong.

Looking forward to your further posts. I encourage you to look next at some
strategic criteria: favorite betrayal, later-no-harm, and later-no-help. I
have strong opinions about which of those are important or not, but I'll let
you take your own look first.

Cheers,

Jameson  

Thanks.

-Benn Grant

eFix Computer Consulting

 <mailto:benn at 4efix.com> benn at 4efix.com

603.283.6601

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